In this paper, a global decentralised adaptive output feedback control is proposed for a class of interconnected nonlinear systems with each subsystem involving not only unknown parameters but also nonlinear terms linear in the unmeasured states, and being preceded with hysteresis nonlinearity described by the saturated PI (Prandtl-Ishlinskii) model. By introducing a modified high-gain observer, together with an initialisation technique, the global stability of the overall closed-loop system can be guaranteed and the [GRAPHICS] tracking performance for each subsystem can be achieved. Furthermore, with a new adaptive law, the restrictive assumption in the existing literature about the upper bound of the strength of the interactions between the subsystems is removed.